Rare nuclear transition provides evidence for stellar explosion mechanism

When the core of a massive star runs out of nuclear fuel, it collapses under its own gravity to form a neutron star or a black hole and sheds its outer layers in a supernova. (See, for example, the article by Hans Bethe, Physics Today, September 1990, page 24 .) However, for smaller stars in the 7- to 11-solar-mass range, gravitational collapse may not be the only possible route to a supernova. Those stars are abundant in our galaxy, but the final phase of their evolution is unclear. Some may undergo gravitational collapse like massive stars. But if nuclear reactions in a star’s core generate sufficient energy to counter collapse, its life may also end in a thermonuclear explosion that ejects some material while leaving behind a white dwarf remnant.

To understand the fate of a star, astrophysicists must delineate the nuclear reactions that occur in its core after the main fuel-burning cycle ends. At that point, stars in the range of 7–11 solar masses have cores that consist mainly of oxygen and neon. Theoretical models of stellar evolution predict which reactions happen next. Particularly important is a reaction sequence in which an atomic nucleus absorbs an electron, which combines with a proton to form a neutron. In that sequence, a high-energy (7 MeV) electron is absorbed by neon-20 to form fluorine-20, which promptly captures another electron to form oxygen-20. As a by-product of that reaction chain, gamma radiation is released and heats the stellar core enough to trigger the ignition of oxygen. Whether the energy liberated by oxygen ignition is enough to forestall collapse or trigger an explosion depends critically on the density at which the onset of electron capture on ²⁰Ne takes place.

A team led by Oliver Kirsebom (now at Dalhousie University in Nova Scotia, Canada) and Gabriel Martínez-Pinedo (GSI Helmholtz Center for Heavy Ion Research and Technische Universität Darmstadt in Germany) has recently found that the electron capture on ²⁰Ne occurs at lower densities and with a higher rate than previously expected. The researchers inferred experimentally the chain’s first and rate-limiting step—the capture of electrons by ²⁰Ne—under conditions that prevail in a stellar interior. Stellar models based on the new rate suggest that thermonuclear explosion is the common end for many of our galaxy’s stars. ^{1 , 2}

Forbidden transition

Atomic nuclei have different energy states. Which one a nucleus is most likely to inhabit depends on the temperature and density of the environment. At the temperatures in oxygen–neon stellar cores, most ²⁰Ne exists in its ground state. As the stellar core evolves, its density grows and the energy of the electrons, which comprise a degenerate gas in the core, increases. At some point, electrons will have enough energy, 7 MeV, to link in a decay chain the ground states of Ne and F.

The rate at which Ne captures electrons during the transition between the ground states of ²⁰Ne and ²⁰F nuclei can be directly related to the inverse process, the beta-decay in which radioactive ²⁰F emits an electron and produces ²⁰Ne. Under terrestrial conditions, ²⁰F decays to the first excited state of ²⁰Ne. However, that ground state transition has an extremely low likelihood and is considered forbidden. Forbidden means that the reaction links nuclear states with different spins, which results in a transition that is, in this case, supressed by six orders of magnitude compared to an allowed transition between same-spin states. As a result, quantifying the rate-limiting electron capture step is difficult.

To learn more about the neon–fluorine electron capture rate, Kirsebom and colleagues looked to an allowed version of the inverse beta-decay process. The decay that connects ²⁰F decays to the first excited state of ²⁰Ne can produce electrons that have from zero to 5.4 MeV of kinetic energy, whereas the decay connecting the ground states of ²⁰F and ²⁰Ne produces electrons up to a maximum kinetic energy of 7 MeV. ³ Electrons with energies up to 5.4 MeV mostly originate from the allowed decay to the excited state of ²⁰Ne; but any electrons with energies above 5.4 MeV must originate through the forbidden ground state decay. Kirsebom designed an experiment to measure how frequently ²⁰F emitted electrons with energies above 5.4 MeV, and thereby determine the strength of the forbidden transition.

Earthly measurements

Because ²⁰F decays extremely rapidly, with a half-life of 11 seconds, studying its behavior requires an advanced accelerator facility where the isotopes can be produced and quickly transported to a detection system. At the University of Jyväskylä accelerator laboratory in Finland the researchers bombarded carbon foil with a beam of ²⁰F nuclei. The laboratory is one of the few facilities worldwide that can produce a pure, intense, low-energy ²⁰F beam, free of contamination by other radioactive isotopes. On striking the carbon foil, the ²⁰F nuclei became embedded. Kirsebom and his colleagues, shown in figure 1, monitored the nuclei as they decayed and emitted energetic electrons. A specially designed scintillator detector with a magnetic transporter measured the electrons’ energies.

Figure 1.

The team paid particular attention to electrons that had kinetic energies 5 MeV and above. The resulting energy spectrum in figure 2 shows the count of electrons emitted at each energy during 105 hours of data collection. For energies below 5.4 MeV, the electron count exceeded by five orders of magnitude that emitted by background sources. The spectrum matched that obtained by simulations, which indicated frequent occurrence of the allowed decay of ²⁰F to excited ²⁰Ne. The background count rate was determined in separate measurements made with precisely the same setup but without the ²⁰F beam. Between 5.4 MeV and 7.0 MeV, the measured number of counts exceeded that expected from background sources. Electrons at those energies indicate occurrence of the forbidden decay of ²⁰F to ground state ²⁰Ne. For energies above 7 MeV, the entire electron count came from background cosmic rays. “Just looking at the large number of counts observed, one realizes that we are dealing with a rather strong forbidden transition,” says Kirsebom.

Figure 2.

The researchers concluded that 1 in 250 000 events produced ²⁰Ne in its ground state—a rate that should match that of the reverse process. Based on the measured transition probability, and considering stellar plasma densities of 10⁹ g/cm³, electron capture on ²⁰Ne was determined to occur eight orders of magnitude more often than assumed by previous calculations.

Stellar implications

Numerical simulations of stellar evolution that take into account the newly measured Ne–F transition rate suggest that the star’s core begins to generate heat earlier than previous models predicted. ⁴ Once the core reaches 1.5 × 10⁹ K, oxygen can fuse with itself; the earlier ignition happens, the higher the likelihood of a thermonuclear explosion.

The resulting supernova, like the one simulated in figure 3, differs from the type II supernova that ends the life of a star more massive than 11 solar masses. It also differs from the type Ia supernova in which a carbon–oxygen white dwarf fully explodes. It ejects more mass and it leaves behind an iron-rich white dwarf, as opposed to a neutron star or black hole. ⁵ The proportion of ejected elements also differs from both other supernova types; it is richer in calcium-48, titanium-50, chromium-54, and iron-60.

Figure 3.

By itself, a high Ne–F transition rate isn’t enough to preordain the explosion of a 7- to 11-solar-mass star. The energy released by electron capture on ²⁰Ne may trigger convection in the stellar core. Convection leads to mixing and could delay the onset of oxygen ignition, so that gravitational collapse would be the end of the star. Improved models of convection in the stellar core are needed.

The observation of iron-rich white dwarfs would clinch the case that the Ne–F transition drives a thermonuclear explosion. Several candidates have already been detected through observations of their atmospheres. ⁶ The associated explosions are expected to be characterized by specific spectral features that could, in principle, be observed. ⁵